Play with this applet by Bob Allanson.

1. Move the triangle vertices around to convince yourself that the nine-point circle idea is valid.

2. Can you make the nine-point circle degenerate to a 'six-point' (distinct) circle? a 'four point' circle?      any other number of points less than nine? Describe the nature of the triangle in each case.

3. Click on the extension box. What appears to be true in this case?